%2B(x%5E2-8x%2B10).jpeg "(6x^2-3x-1)+(x^2-8x+10)")
Simplifying Polynomial Expressions: (6x^2 - 3x - 1) + (x^2 - 8x + 10)
In mathematics, simplifying polynomial expressions is a fundamental skill. This involves combining like terms and reducing the expression to its simplest form. Let's explore how to simplify the expression (6x^2 - 3x - 1) + (x^2 - 8x + 10).
Understanding the Concepts
- Polynomials: These are algebraic expressions consisting of variables and coefficients, combined using addition, subtraction, and multiplication.
- Like terms: Terms with the same variables raised to the same powers.
Steps to Simplification
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Remove Parentheses: Since we are adding the two polynomials, the parentheses are not necessary.
(6x^2 - 3x - 1) + (x^2 - 8x + 10) = 6x^2 - 3x - 1 + x^2 - 8x + 10
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Identify Like Terms: Group the terms with the same variables and powers.
(6x^2 + x^2) + (-3x - 8x) + (-1 + 10)
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Combine Like Terms: Add or subtract the coefficients of the like terms.
7x^2 - 11x + 9
The Simplified Expression
Therefore, the simplified form of the expression (6x^2 - 3x - 1) + (x^2 - 8x + 10) is 7x^2 - 11x + 9.